January 2001
Staying Power
| "The best way to suppose what may come, is to remember what is past." |
| -- George Savile |
ANY QUANTITATIVE MODELS SUFFER from momentum bias. Their reliance on past performance causes them to forecast the continuation of the most recent trends. In essence, what did well recently will continue to do so. If cyclical stocks were the top performers, the model will favor them over defensive issues, even if the economy has slowed.
So what about our models? Do they have this problem? They're certainly quantitative, being based on multiple regressions. They're also based on 
historical performance as determined by eight fundamental factors. Does that mean they're based on recent momentum?
Portfolio 3 is inherently momentum based. Its model runs a single regression across all the stocks in the S&P 500. Every two months the screen is rerun and the portfolio is updated. This is a fairly short-term outlook and depends on the momentum of the prior period. This model isn't momentum biased, it's momentum dependent -- but then that's what it's designed to be.
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 Source: Baseline As predicted, Quintile 1 (the current P4) outperformed all other quintiles over the fifteen year period ending November 30, 2000. In addition, each quintile performed in descending order, exactly as expected. |
Portfolio 4 is a more interesting case. Its model runs separate regressions on each sector of the S&P 500. The underlying belief is that relevant factors differ from sector to sector. Unlike P3, this portfolio is initially sector weighted with the inclusion of the top screeners from each sector. Once selected, stocks will only be removed from the portfolio if deleted from the S&P 500
The Test
In light of this longer-term time horizon, momentum bias is a much greater concern for P4. If it simply reflects the short-term performance of its factors just before the initial screen, it runs the risk of underperformance when the market, the economy, and the factors themselves experience changes.|
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 Source: Baseline Over the past twelve months (ending November 30, 2000) the quintiles have again performed as expected. In fact, a great deal of P4's outperformance has occurred in the last several years. |
Like quants always do, we turned to historical performance to test the model. We divided the S&P 500 into five "quintiles". The first was P4, as it is currently constituted. The second quintile (P4Q2) is the next 25% of the highest screeners in each sector. The third quintile (P4Q3) is the next highest 25%, P4Q4 the next, and the fifth quintile (P4Q5) represents the lowest 25% from each sector.
Next, we looked at the past 15 years' performance (December 1, 1985 - November 30, 2000) for each quintile. (Fifteen years was used for this study since this is the extent of our Baseline data.) If the model really works, you'd expect them to perform in order with the top quintile outperforming the rest, P4Q2 next in order and P4Q5 on the bottom.
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One thing distinguishing this test from most "backtests" is the fact that we did not reconstitute the quintiles over time. In other words, we calculated the performance of the quintiles as they are presently constituted. As a result, the performance shown for P4 (or any quintile for that matter) is what you would have actually received if you had held the present mix over the past 15 years
The Results
As the nearby graph illustrates, P4 led all other quintiles over the 15-year period. In addition, each of the other quintiles performed as expected with overall returns in descending order. If this is momentum, it's long-term momentum.Of course most of the gain for all quintiles occurred along with the run-up in growth stocks over the last several years. During that time, P4 was up 555% and P4Q2 was up 238% while the two lowest quintiles were up only 69% and 30%, respectively. Is it possible that P4's 15-year lead was built in that short time span?
To test this, we decided not to look at the annual performance in each of the 15 years. Instead, we considered rolling 5-year periods that are a better proxy for P4's long-term investment horizon.
As you probably know, to create 5-year rolling periods, you simply start with the first five years (December 1, 1985 - November 30, 1990) as the first period. To create the next, you add one year and drop the oldest (December 1, 1996 - November 30, 1991). Additional periods are developed in the same manner. With 15 years to work with, we were able to create ten 5-year periods.
The results are shown in the accompanying chart. In each of these periods, P4 was the leader, followed by P4Q2 and then P4Q3. This was exactly as predicted.
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Period Performance | ||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||
For each of the eleven 5-year rolling periods ending November 30th, P4 (Quintile 1) outperformed all other quintiles. With the exception of periods ending 1992-1998 when P4Q4 underperformed P4Q5, the order of performance was as expected. |
The only twist in the model occurred in the rolling periods ending in 1992-1998. In each of them, P4Q5 slightly outperformed P4Q4. The anticipated order held in the other four periods.
The Conclusions
At the very least, our model would have performed very well over the past fifteen years. It's hard to make a case that this could have been solely momentum based given that the market and the economy went through events ranging from the crash of 1987 to last year's tech run-up, from the banking crisis of the late '80s to the irrational exuberance of the late '90s. Again, if this is momentum, it's long-term momentum.The failure of P4Q4 to outperform P4Q5 suggests the model fails to adequately distinguish between poorer performers. They may correlate differently with the eight independent factors, or may require additional ones. At any rate, unless you're a short seller, you wouldn't be interested in the lower quintiles anyway.
Frankly, we were a little surprised at how well this model tested. For a first pass, it would appear to be a good start.
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